Problem: The grades on a geometry midterm at Loyola are normally distributed with $\mu = 65$ and $\sigma = 4.5$. William earned a $59$ on the exam. Find the z-score for William's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for William's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{59 - {65}}{{4.5}}} $ ${ z \approx -1.33}$ The z-score is $-1.33$. In other words, William's score was $1.33$ standard deviations below the mean.